A table is shown with two rows and two columns. The horizontal side is labeled negative 4 x superscript 4 baseline and 10 x while the vertical side is labeled 5 x cubed and negative 1.

Question

A table is shown with two rows and two columns. The horizontal side is labeled negative 4 x superscript 4 baseline and 10 x while the vertical side is labeled 5 x cubed and negative 1.
Find the product when you multiply the polynomials  (−4x4+10x)(5x3−1) .

(1 point)
Responses

−20x7+50x4−6x
negative 20 x superscript 7 baseline plus 50 x superscript 4 baseline minus 6 x

−20x7−54x4−10x
negative 20 x superscript 7 baseline minus 54 x superscript 4 baseline minus 10 x

−20x7+54x4−10x
negative 20 x superscript 7 baseline plus 54 x superscript 4 baseline minus 10 x

20x7+54x4−10x
20 x superscript 7 baseline plus 54 x superscript 4 baseline minus 10 x
Skip to navigation

GPT-4o mini · Answer

To find the product of the polynomials $(-4x^4 + 10x)(5x^3 - 1)$, we can use the distributive property (also known as the FOIL method for binomials). 1. Multiply each term in the first polynomial by each term in the second polynomial: $$ (-4x^4)(5x^3) + (-4x^4)(-1) + (10x)(5x^3) + (10x)(-1) $$ 2. Now, perform the multiplications: - First term: $(-4x^4)(5x^3) = -20x^7$ - Second term: $(-4x^4)(-1) = 4x^4$ - Third term: $(10x)(5x^3) = 50x^4$ - Fourth term: $(10x)(-1) = -10x$ 3. Now, add all the terms together: $$ -20x^7 + 4x^4 + 50x^4 - 10x $$ 4. Combine like terms: - The $x^4$ terms: $4x^4 + 50x^4 = 54x^4$ So, the final expression becomes: $$ -20x^7 + 54x^4 - 10x $$ The correct answer is: $-20x^7 + 54x^4 - 10x$ (which matches the third response option).